Commuting Codazzi tensors and the Ribaucour transformation for submanifolds

2003 ◽  
Vol 44 (3-4) ◽  
pp. 258-278 ◽  
Author(s):  
Marcos Dajczer ◽  
Ruy Tojeiro
Keyword(s):  
Codazzi Tensors

A note on Codazzi tensors

2014 ◽  
Vol 362 (1-2) ◽  
pp. 629-638 ◽  
Author(s):  
Giovanni Catino ◽  
Carlo Mantegazza ◽  
Lorenzo Mazzieri
Keyword(s):  
Codazzi Tensors

Some theorems on Codazzi tensors

1986 ◽  
Vol 191 (4) ◽  
pp. 575-584
Author(s):  
Li An-Min
Keyword(s):  
Codazzi Tensors

scholarly journals Hypersurfaces and Codazzi tensors

2008 ◽  
Vol 154 (1) ◽  
pp. 51-58 ◽  
Author(s):  
Thomas Hasanis ◽  
Theodoros Vlachos
Keyword(s):  
Codazzi Tensors

scholarly journals Codazzi tensors and reducible submanifolds

1981 ◽  
Vol 268 (1) ◽  
pp. 231-231
Author(s):  
Irl Bivens
Keyword(s):  
Codazzi Tensors

PSEUDO-Q-SYMMETRIC RIEMANNIAN MANIFOLDS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350013 ◽  
Author(s):  
CARLO ALBERTO MANTICA ◽  
YOUNG JIN SUH
Keyword(s):  
Riemannian Manifolds ◽  
Symmetric Spaces ◽  
State Equation ◽  
Space Time ◽  
Local Form ◽  
Dimensional Manifold ◽  
Conformally Flat ◽  
Metric Tensor ◽  
Symmetric Manifold ◽  
Codazzi Tensors

In this paper, we introduce a new kind of tensor whose trace is the well-known Z tensor defined by the present authors. This is named Q tensor: the displayed properties of such tensor are investigated. A new kind of Riemannian manifold that embraces both pseudo-symmetric manifolds ( PS )n and pseudo-concircular symmetric manifolds [Formula: see text] is defined. This is named pseudo-Q-symmetric and denoted with ( PQS )n. Various properties of such an n-dimensional manifold are studied: the case in which the associated covector takes the concircular form is of particular importance resulting in a pseudo-symmetric manifold in the sense of Deszcz [On pseudo-symmetric spaces, Bull. Soc. Math. Belgian Ser. A44 (1992) 1–34]. It turns out that in this case the Ricci tensor is Weyl compatible, a concept enlarging the classical Derdzinski–Shen theorem about Codazzi tensors. Moreover, it is shown that a conformally flat ( PQS )n manifold admits a proper concircular vector and the local form of the metric tensor is given. The last section is devoted to the study of ( PQS )n space-time manifolds; in particular we take into consideration perfect fluid space-times and provide a state equation. The consequences of the Weyl compatibility on the electric and magnetic part of the Weyl tensor are pointed out. Finally a ( PQS )n scalar field space-time is considered, and interesting properties are pointed out.

Harmonic Gauss maps and Codazzi tensors for affine hypersurfaces

1990 ◽  
Vol 55 (3) ◽  
pp. 298-305 ◽  
Author(s):  
Yi -Bing Shen
Keyword(s):  
Gauss Maps ◽  
Codazzi Tensors

THE STRUCTURE OF CERTAIN RIEMANNIAN MANIFOLDS ADMITTING CODAZZI TENSORS

1994 ◽  
Vol 27 (1) ◽  
Author(s):  
Andrzej Ge̖barowski
Keyword(s):  
Riemannian Manifolds ◽  
Codazzi Tensors
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